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Basic Algebra

Help in solving algebra problems

I am trying to help my grandson with is home work and I am not much help to him. "Can you help me with solving these problems?" Perform the following operation with fractions: 1. 7 1 -- +-- = 9 3 2. 3 1 -- - -- = 4 6 3. 7 6 -- *-- = 4 11 4 1 1 -- -:- -- =

Inner Product, Linear Space, Constant Polynomial and Mean Square Deivation

Let C[1,3] be the (real) linear space of all real continuous functions on the closed interval [1,3], equipped with the inner product defined by setting <f,g> := 1&#8747;3f(t)g(t)dt, f,g E C[1,3]. Let f(t) = 1/t, t E [1,3]. (i). Show that the constant polynomial g which best approximates f on [1,3] (in the sense of least

Stereographic Projection, Riemann Sphere and Mapping

A plane is inserted through the equator of a unit sphere. A point on the sphere is mapped onto the plane by creating a line from the point on the sphere, through the north pole, where this line hits the plane is the projection of the point. Show that circles on the sphere map to circles on the plane except when the circles run

Conjugacy

Let the dihedral group D_n be given by elements "a" of order "n" and "b" of order 2, subject to the identity b*a=a^-1*b. Prove that a^m is conjugate to only a^-m, and that a^m8b is conjugate to a^(m+2k)*b, for any integer k.

Propagation of Error

(See attached file for full problem description and equations) --- A 100 uL (microLiter) sample of a 7.0 millimolar protein is diluted to 500.0mL. If the error in measurement of the molarity(M) is ±0.02 mM, of the uL pipet is ±1 uL, and of the volume of the 500 mL flask is ±0.15 mL, determine how the molarity of the resul

Borel-measurable function

Prove that the following function is Borel-measurable function. f_n(t) = { [t*2^n]*2^-n , 0 < t < n, n , t > or = to n | f_n(t) - t | < 2^-n , t < n } I want a detailed proof. I want to kn

Factorization

Divide (x^2+6x+8) by (x+2)/(x+1). Reduce to lowest terms.

Solving 3 Quadratic Equations : Optimum Methods

I had a 50 problem assignment, and have 3 questions that I either want to check my answers with a tutor, or had no idea how to figure them out. I have attached a Microsoft Word document, and would prefer getting that sent back to me with the work and answers shown so that I can understand it. Thank You! --- (See atta

Solve

1. Simplify: Remove the symbols of grouping and combine like terms. 5[3(4x - 2) - 3(6 - x)] + 7 2. Subtract (18x2 - 5x + 4) from (3x2 - 3x - 8) 3. Simplify: (27a3 b6 )2/3 4. Simplify: (102x+1)(104x) 5. Simplify and express your answer with positive exponents only. #6 & 7: Perform the indicated o

Radical expressions

6 2/3 (8x ) 5 9 3 sq root. 24X y 3 sq root. 1 ___ 2 2X Solve for X 10X-2(5-X) = 7X-2(3+x)

Algebra equations

(See attached file for full problem description with equations) --- 1. Perform the following computation. Write the answer in scientific notation. 2. Perform the indicated operation. Solve for x. Reduce your answer to lowest terms. 3. Perform the indicated operation. 4. Solve this equation. Solve for x. 5. S

Irreducible representations of a quaterion subgroup

Let G be the subgroup of quaternions of 8 elements, that contains ±1, ±i, ±j, ±k with relations i^2=j^2=k^2= &#8722;1, ij=k, jk=i, ki=j, ij=&#8722;ji, ik=&#8722;ki, jk=&#8722;kj. Classify irreducible representations of G over C.

Solving Equations (4 Problems)

Solve equation. Watch for extraneous solutions #30 6 + 7 =y-1 y-2 y-8 y-8 Solve equation and check for extraneous solutions # 35 square root oft 2t+4= square root of t-1 Solve each equation #88 square root 9x2= x+6 Solve each equation by using the quadratic formula. 3z2-8z+2=0 ---

Factoring a Cubic Equation

Question: Each of the three dimensions of a cube with a volume of x^3 cubic centimeters is increased by a whole number of centimeters. If the new volume is x^3 + 10x^2 + 31x + 30 cubic centimeters and the new height is x + 2 centimeters, then what are the new length and width?